Differentiability of Mather's $\beta$-function vs Ma\~n\'e's conjecture
Dynamical Systems
2013-04-04 v1
Abstract
We prove that if a time-periodic Tonelli Lagrangian on a closed manifold satisfies a strong version of the Differentiability Problem for Mather's -function, then the Legendre transforms of rational homology classes are dense in the first cohomology of , which is a first step towards Ma\~n\'e's conjecture.
Cite
@article{arxiv.1304.0868,
title = {Differentiability of Mather's $\beta$-function vs Ma\~n\'e's conjecture},
author = {Daniel Massart},
journal= {arXiv preprint arXiv:1304.0868},
year = {2013}
}